Try making small shims out of pieces of matchbook cover and placing them in the nut slots under the strings. If this makes the buzz go away, your nut slots were cut too low. You can make a more permanent fix by placing a drop of superglue in each nut slot. It's a common guitar repair, but not exactly a legit repair in the doublebass world.
If cheating the nut slots higher doesn't fix the problem, it could be a technique issue or your fingerboard could have inadequate camber. A luthier can fix that for a few hundred bucks, but go to a bass luthier or a good violin shop, not Joe Bob's Geetar Fix-It.
"All of the poor people who started rock and roll are cool." -- Iggy